1
1.
Ludwig Boltzmann theorized that the entropy of a state is related to the number of
ways that state can be achieved.
This is the probabilistic interpretation of entropy.
The
equation that describes this theory is S=k lnW.
To investigate the consequences of this
equation consider a doublechambered flask containing 8 atoms (see the figure below).
Each atom, numbered 1 – 8, can be in either the left chamber (L) or the right chamber
(R).
For our purposes, there are 9 different states of the system:
{8L, 0R; 7L, 1R; 6L,
2R; . . .; 0L, 8R}, where the integer denotes the number of molecules in the specified
side.
Importantly, each state is not unique.
For example, there are 8 different ways
forming the state {7L, 1R}.
For this state W = 8.
(a)
Calculate W and S for each of the 9 different states of the system.
Explain your
reasoning.
Express your final answer in a table.
(b)
Graph S as a function of number of molecules in the left chamber.
(c)
Suppose you cool the lefthand side of the flask down to absolute zero, which will
cause all of the gas molecules to condense on the lefthand side.
Does this spontaneous
ordering violate the second law of thermodynamics? Explain.
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 Spring '07
 DAVIS,F
 Chemistry, Thermodynamics, Entropy

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